Beta function series help pls

Hi everyone!
I got two versions of one particular function and now I need to show those two versions are equivalent.
For that I need to show the follwing,


Attachment 24207


Can please try to show that the above two are equivalent, I think beta function series formulas should have been utilized, but I don't know how to do ti as I am poor in mathematics.


Please Help Me.


Thank you.

In the sum it should be k, not i. Have you tried a proof by induction on n?